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Keywords:

  • second-generation wavelet grid refinement;
  • non-dyadic grids;
  • adaptive multigrid;
  • singular perturbation;
  • MOSFETs;
  • quantum tunnelling;
  • density-gradient equation

Abstract

In this manuscript, we introduce a second-generation wavelet thresholding technique used to construct a numerically stable non-dyadic sparse grid representation. The resulting second-generation wavelet projectors, when coupled to a multigrid solver, provide an elegant method for integrating the numerical solution. The combined method is then utilized in the solution of a singular perturbation problem that arises when modelling an n-MOS gate exhibiting quantum tunnelling. The resulting solution is compared with the full Schrödinger–Poisson system, and the two solutions are shown to be in good agreement. Copyright © 2006 John Wiley & Sons, Ltd.